On the Probability Density Function of the Squared Envelope of a Sum of Random Phase Vectors
M.K. Simon · IEEE Transactions on Communications · 1985
A recursive solution is presented for the probability density function of the sum ofNindependent, random phase vectors. The recursion parameter isN, the number of vectors in the sum. This approach allows one to rapidly compute a complete set of these density functions for values ofN = 2, 3, ..., N_{max}, where Nmaxtypically corresponds to the total number of system users in a multiuser FHMA/MFSK application, or one plus the total number of jamming tones in an FH/MFSK spread-spectrum application. Such evaluations are necessary for exact calculation of the average error probability performance of such systems.